Pola Sommers, a massage therapist, needs 44 ounces of a 2020 % lavender oil solution. She has only 55 % and 3030 % lavender oil solutions available. How many ounces of each should Pola mix to obtain the desired solution?

Answer: 2.4 ounces of the 30% solution and 1.6 ounces of the 5% solution.

Step-by-step explanation: Every number is written two times.

Pola needs 4 ounces of 20% lavender oil solution, and she has only 5% and 30% oil solutions, so she needs to mix them.

If X is the number of ounces of 5% solution, and Y is the number of ounces of the 30% solution, we have that:

X + Y = 4

(X*0.05 + Y*0.30) / (X + Y) = 0.20

Where I used the percentages in the decimal form because the math is easier.

From the first equation, we can isolate one of the variables, and replace it in the other.

X = 4 - Y

((4-Y) * 0.05 + Y*0.30) / (4 - Y + Y) = 0.20

(4*0.05 + Y * (0.25)) / 4 = 0.20

Y*0.25 = 0.8 - 0.20 = 0.60

Y = 0.60/0.25 = 2.4

So she needs to use 2.4 ounces of the 30% solution, and the other 1.6 ounces are from the 5% solution.